ON A 



NEW METHOD 



PLANNING RESEARCHES 



REPRESENTING TO THE EYE 



Results of Combination of three or more Elements 



IN VARYING PROPORTIONS. 



"7 

ROBERT H. THURSTON, 

OF lIOBOKEJf, N. J. 



[From the Proceedings of the American Association for the Aclvancenicnt of Science, 
(Nashville, iSreefinir, Aug.. 1877.) Vol. XXVI.J 



SALEM: 
PRINTED AT THE SALKM PRESS. 

1878. 



^ 



i^ 



-1 



ON A 

NEW METHOD 

OF 

PLANNING RESEARCHES 

AND OF 

REPRESENTING TO THE EYE 

THE 

Results of Combination of three or more Elements 
IN VARYING PROPORTIONS. 



ROBERT H. THURSTON, 

OF HOBOKEN, X. J. 

1 




[From the Proceedings of the American Association for the Advancement of Science, 
(Nashville, Meeting, Aug., 1877.) Vol. XXVI.J 



ALEM:..-^- 



S. 
PRINTED AT THE SALEM PRESS. 

1878. 



. V 






^'ii79.i 



On a New Method of Planning Researches and of Repre- 
senting TO THE eye the RESULTS OF COMBINATION OF THREE 

OR MORE Elements in Varying Proportions. By R. H. 
Thurston, of Hoboken, N. J. 

I. The writer has lately been called upon to conduct, in the 
mechanical laboratory of the Stevens Institute of Technology, 
among other researches, a series of investigations of the mechan- 
ical properties of the more important alloys of the useful metals. 

The most extended and important of these investigations was 
made at the request of a Committee of the Board appointed by 
the President of the United vStates, by direction of Congress, to 
determine by test, the values, for purposes of construction, of 
iron, steel, and other useful metals and their combinations. This 
"■committee on the metallic alloys" was directed to report upon 
the ''characteristics of alloys and the laws of combination." 

The research entrusted to the writer was the study of the met- 

(lU) 



115 ELEMENTS IN VARYING PROPORTIONS; 

als, copper, zinc, and tin, and their innumerable combinations. 
The planning and the prosecution of the examination of alloys 
composed of two metals, as copper and tin, or copper and zinc, 
was attended with no special difficulties. A series of alloys of 
each of these pairs of elements was made, containing from one 
hundred per cent, copper, at the one end, to one hundred per cent, 
tin, or one hundred per cent, zinc, at the other end of the series, 
and varying by two and a half per cent, from one end to the other. 
The moduli of rupture by transverse stress, by tension, by com- 
pression and by torsion, the moduli of elasticity, the density, ho- 
mogeneousness, the resilience and other properties of all the metals 
in these series were determined and recorded. The results of each 
test of each metal were then plotted and the curve formed by unit- 
ing the points thus laid down represented the law of variation of 
distortion of the piece with variation of the distorting force. Such 
curves may usually be represented, also, by equations which are 
the mathematical expressions of these laws. 

Another set of curves was formed by plotting the results of 
tests of the metals in series. The ordinates of one of these curves, 
for example, measured the tenacity of the allo3-s of the series 
which it referred to, and the abscissas measured the corresponding 
position of the alloy in the series. The abscissa of a certain 
point would thus indicate that the alloy represented Avas midway" 
in the series, containing fift}^ per cent, of each metal, and its ordi- 
nate would show its tenacity to be, say 40,000 pounds per square 
inch of original section. These curves were curiously unsymmet- 
rical and could not be represented b}^ any simple equation ; they, 
however, are none the less valuable as graphical representations 
of the properties of the alloys as grouped in series. An elaborate 
report upon this work has been prepared by the writer for publi- 
cation by the Board from which report the constants thus deter- 
mined may be obtained. 

The properties of any series composed of variable proportions 
of two elements may thus be readily determined and represented ; 
the curves representing the results are also representative of the 
properties of all possible alloys of the two metals. 

II. To determine the properties of all the infinite number of 
possible combinations of the tln-ee metals in triple alloys of copper, 
zinc, and tin seemed, at first, a far less simple matter. It was pro- 
posed to test, first, a set of these alloys diflfering by ten per cent. ; 



BY ROBERT H. THURSTON. 



116 



and the following series was made up to be tested in tension, tor- 
sion and compression, and by transverse stress : — 



COPPER. 


ZIXC. 


TIN. 


COPPER. 


ZINC. 


TIN. 


10 


10 


80 


30 


40 


30 


10 


20 


70 


30 


50 


20 


10 


30 


60 


30 


60 


10 


10 


40 


50 


40 


10 


50 


10 


50 


40 


40 


20 


40 


10 


60 


30 


40 


30 


30 


10 


70 


20 


40 


40 


20 


10 


80 


10 


40 


50 


]0 


20 


10 


70 


50 


10 


40 


20 


20 


60 


50 


20 


30 


20 


30 


50 


50 


30 


20 


20 


40 


40 


50 


40 


10 


20 


50 


30 


60 


10 


30 


20 


60 


20 


60 


20 


20 


20 


70 


10 


60 


30 


10 


30 


10 


60 


70 


10 


20 


30 


20 


50 


70 


20 


10 


30 


30 


40 


80 


10 


10 



It was not sufficient, however, to test this series and simpl3^ to 
record the results. It was necessary to determine the law con- 
necting the mechanical properties with the composition of the 
alloy, to determine whether there were abrupt variations of prop- 
erties, to detect points of maxima and minima and to so accurately 
determine these points, that any one studying the results of the 
work should be able to say, with confidence, what would be the 
precise character of any possible alloy of the three metals which 
he might propose to make. 

It seemed to the writer evident that the only system of collating 
results which would probably enable him to attain these essential 
objects was some graphical method. To represent with satisfactory 
precision, completeness and intelligibility, a series of researches on 
the character of triple alloys of all desired proportions, appeared, 
at first, a most difficult, if not insolvable problem. A very perfect 
and most satisfactory method was, however, finally devised : — 

In any triangle, as at A, figure 1, let fall perpendiculars upon 
the three equal sides. The area of the whole triangle B, C, D, is 
measured by the product of the altitude, C E, by one-half the 
base, B D. Draw lines A B, AC, AD, to the vertices of the 




117 ELEMENTS IN VARYING PROPORTIONS; 

triangle, thus forming three smaller triangles, the sum of which 
equals, in area, the original triangle. We now have : C E X 1-2 
B D = A F X 1-2 B D + A G X 1-2 
B C + A H X 1-2 C D ; or, the sides 
of the triangle being equal, C E X 
1-2BD=(AF4-AG + AH) 
1-2 B D. Hence, A F + A G -}- 
A H = C E. 

But the area of the whole triangle 
may be conceived to represent a triple ^ 
alloy composed of the three compo- ^ £ 

nents in proportions represented by 
tlie areas of the three several small '°"^^ 

triangles which together make up its total area. But these 
smaller triangles have areas proportional, as has just been seen, 
to their altitudes, A F, A G, A H, the proportions in which the 
three metals are combined to form the given triple alloy may, 
therefore, be measured by the ratio of their representative tri- 
angles to the whole triangle in area and in altitude. Then, 
dividing the height of the large triangle into one hundred equal 
parts, the altitudes of the small triangles, measured in the same 
units, will represent the percentages of the three elements in the 
given alloy. 

A moment's thought will show that we have here precisely what 
is needed. Ever}' point in the triangle thus represents some cer- 
tain triple alloy ; there is no possible triple alloy which has not its 
representative point in our triangle. , We now have before us a 
field which exactly defines our research, and we may attempt its 
exploration with a clear understanding of what is to be done. Its 
topography may be studied as systematically and completely as 
that of any other territory of which the exact boundaries have been 
determined and marked out. 

Although it is entirely beyond our power, even if we desired to 
do so, to examine every point in this great field and to make every 
one of the infinite number of alloj^s here represented, and then to 
determine the principal characteristics of each by direct experi- 
ment, we may arrive at the same result, as nearly as we may 
choose, by the same system which we adopt in all topographical 
surveys. Let it be proposed to discover what is the strength of 
all the possible alloys of copper, zinc and tin : lay out, M'ithin the 



TTIS- 



BY ROBERT H. THURSTON. 



118 




principal figure, a series of concentric triangles, as in figure 2, of 
which the vertices are placed at distances representing ten per 
cent., twenty per cent., thirty per cent., and so on, from the ver- 
tices of the large triangle ; select along the sides of tliese trian- 
gles excluding the exterior figure, points ten per cent, apart for 
examination. These points will be found to represent the list of 

triple alloj^s which has al- 
ready been given above. 
The points taken in the 
outline of the principal tr,i- 
angle represent the double 
alloys of copper-zinc, cop- 
per-tin, and tin-zinc, in 
proportions also varjdng 
ten per cent. They are al- 
loys in each of which the 
proportion of the third ele- 
ment of the variable triple 
combination to be studied 
has become zero. Now, 
determine the strength of 
each of these allo3'S, and, upon the point which represents it in the 
figure, erect a perpendicular having a height proportional, on an}'- 
convenient scale, to that strength. Having completed this work, 
we have, upon our triangular base-plane, a forest of verticals, each 
of which is an ordinate of a point in a surface which may now be 
conceived to pass through them all. Curves of sections, running 
in any desired direction across this field, may now be made, and 
they will be the graphical representations of the law which con- 
nects cohesion and composition in the series of alloys so selected ; 
just as the surface is representative of the law for all possible 
alloys of the three metals selected for experiment. 

Lines connecting points of equal altitude may be drawn, as on 
topographical maps, and, on these lines of alloys of equal strength, 
that which meets an3^ given requirement in other respects, as in 
cheapness or in ductilit}^, may be selected. The same method will 
evidently answer equally well in the representation of any other 
qualit}'', as the resistance to transverse fracture, to shearing forces, 
to compression, or in the exhibition of ductility, elasticity, or of 



Figure 2, 



119 



ELEMENTS IN VARYING PROPORTIONS ; 



the values of the moduli of elasticity or of resilience whether elas- 
tic or total. 

In many cases, it would be found that, at sharp culminations, in 
points or lines, forming peaks or ridges in our topography, it would 
be necessary to take another set of points nearer together, and 
thus to feel out with greater exactness the sudden changes of re- 
sult which follow the operation of the discovered law at such " crit- 
ical" points or lines. 

The result of an investigation, such as has just been described, 
may be very beautifully exhibited to the eye by making a model of 




Fisrure 3. 



the surface thus determined. In carrying out these researches the 
writer has found the following plan perfectly satisfactory : — 



BY ROBERT H. THURSTON. 120 

Lay out a triangle, as above described, upon a surface of sheet 
brass. At the points at which determinations have been made, 
erect wires of which the lengths have been made carefully propor- 
tional to the ordinates of the representative surface at those points, 
screwing them firmly, or otherwise fixing them, in their places. 
When all the wires are in place and are found to be of the exact 
length required, place bits of board along the outside to form the 
boundaries of the triangle, and pour in plaster of Paris until the 
wires are all covered. When the plaster has set, remove the boards 
and carefully cut away the upper part of the plaster, working care- 
fully down to the tops of the wires, just exposing their points. The 
surface thus produced is a model of the strength, or other quality 
represented, of all the alloys. 

Mr. M. I. Coster has prepared for the writer such a model of the 
cohesive strength of the alloys of the three metals, copper, zinc, 
and tin, as determined for the United States Board appointed to 
test metals, and a photograph has been taken from which the en- 
graving, figure 3, has been made. A full account of the research 
has been prepared for publication and presented to the Board. It 
will probably be printed by Congress and the constants determined 
may then be obtained. The writer is not at liberty to give them 
here, and the illustration is presented simply as showing well this 
method of investigation of such problems, as it has been practised 
by him. 

[Printed at the Salem Pkess, April, 1878.] 



r.-*:>^-- 



